Given that royal imposters could successfully impersonate kings, (a la Perkin Warbeck) did any commoners ever try to impersonate a member of the nobility?

Yep, definitely happened. Pretending to be a down-on-their-luck nobleman was actually a pretty common confidence trick back in the day, whether one was looking to get handouts from other aristocrats touched by your hypothetical suffering, or trying to pass off fake “heirlooms” as genuine articles that have to be sold off in a moment of need, or trying to finagle your way to marrying the daughter of a wealthy and socially ambitious bourgeois. 

When you get right down to it, nobility ultimately is just a set of mannerisms and cultural capital attached to a certain costume and appearance.